Density-based cluster algorithms for the identification of core sets.

The core-set approach is a discretization method for Markov state models of complex molecular dynamics. Core sets are disjoint metastable regions in the conformational space, which need to be known prior to the construction of the core-set model. We propose to use density-based cluster algorithms to identify the cores. We compare three different density-based cluster algorithms: the CNN, the DBSCAN, and the Jarvis-Patrick algorithm. While the core-set models based on the CNN and DBSCAN clustering are well-converged, constructing core-set models based on the Jarvis-Patrick clustering cannot be recommended. In a well-converged core-set model, the number of core sets is up to an order of magnitude smaller than the number of states in a conventional Markov state model with comparable approximation error. Moreover, using the density-based clustering one can extend the core-set method to systems which are not strongly metastable. This is important for the practical application of the core-set method because most biologically interesting systems are only marginally metastable. The key point is to perform a hierarchical density-based clustering while monitoring the structure of the metric matrix which appears in the core-set method. We test this approach on a molecular-dynamics simulation of a highly flexible 14-residue peptide. The resulting core-set models have a high spatial resolution and can distinguish between conformationally similar yet chemically different structures, such as register-shifted hairpin structures.